casinf, casin, casinl
From cppreference.com
Defined in header <complex.h>
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(1) | (since C99) | |
(2) | (since C99) | |
(3) | (since C99) | |
Defined in header <tgmath.h>
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#define asin( z ) |
(4) | (since C99) |
1-3) Computes the complex arc sine of
z
with branch cuts outside the interval [−1,+1] along the real axis.4) Type-generic macro: If
z
has type long double complex, casinl
is called. if z
has type double complex, casin
is called, if z
has type float complex, casinf
is called. If z
is real or integer, then the macro invokes the corresponding real function (asinf, asin, asinl). If z
is imaginary, then the macro invokes the corresponding real version of the function asinh, implementing the formula asin(iy) = i asinh(y), and the return type of the macro is imaginary.Parameters
z | - | complex argument |
Return value
If no errors occur, complex arc sine of z
is returned, in the range of a strip unbounded along the imaginary axis and in the interval [−π/2; +π/2] along the real axis.
Errors and special cases are handled as if the operation is implemented by -I * casinh(I*z)
Notes
Inverse sine (or arc sine) is a multivalued function and requires a branch cut on the complex plane. The branch cut is conventionally placed at the line segments (-∞,-1) and (1,∞) of the real axis.
The mathematical definition of the principal value of arc sine is asin z = -iln(iz + √1-z2
)
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Example
Run this code
#include <stdio.h> #include <math.h> #include <complex.h> int main(void) { double complex z = casin(-2); printf("casin(-2+0i) = %f%+fi\n", creal(z), cimag(z)); double complex z2 = casin(conj(-2)); // or CMPLX(-2, -0.0) printf("casin(-2-0i) (the other side of the cut) = %f%+fi\n", creal(z2), cimag(z2)); // for any z, asin(z) = acos(-z) - pi/2 double pi = acos(-1); double complex z3 = csin(cacos(conj(-2))-pi/2); printf("csin(cacos(-2-0i)-pi/2) = %f%+fi\n", creal(z3), cimag(z3)); }
Output:
casin(-2+0i) = -1.570796+1.316958i casin(-2-0i) (the other side of the cut) = -1.570796-1.316958i csin(cacos(-2-0i)-pi/2) = 2.000000+0.000000i
References
- C11 standard (ISO/IEC 9899:2011):
- 7.3.5.2 The casin functions (p: 190)
- 7.25 Type-generic math <tgmath.h> (p: 373-375)
- G.7 Type-generic math <tgmath.h> (p: 545)
- C99 standard (ISO/IEC 9899:1999):
- 7.3.5.2 The casin functions (p: 172)
- 7.22 Type-generic math <tgmath.h> (p: 335-337)
- G.7 Type-generic math <tgmath.h> (p: 480)
See also
(C99)(C99)(C99) |
computes the complex arc cosine (function) |
(C99)(C99)(C99) |
computes the complex arc tangent (function) |
(C99)(C99)(C99) |
computes the complex sine (function) |
(C99)(C99) |
computes arc sine (arcsin(x)) (function) |
C++ documentation for asin
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